Open Access Review Article

Solving the Non-Damped Oscillatory Problem with Random Loading Conditions using WHE Technique

Amnah S Al Juhani1* and Aisha M Al Hwiti2

1Tabuk University, Faculty of Science, Saudi Arabia

2Tabuk University, Faculty of Science, Saudi Arabia

Corresponding Author

Received Date: June 10 , 2019;  Published Date: June 17 , 2019


The spectral techniques for solving the stochastic differential equations (SDEs) are efficient compared with other techniques. They can be used to obtain analytical solutions specially in case of linear SDEs. Among which, the Wiener-Hermite expansion (WHE) and the Winer Chaos expansion (WCE) are the most common. WHE is more efficient as it depends directly on a basis that is directly dependent on the noise process. It can be used efficiently when the SDE is forced by additive and/or multiplicative noise.

In the current work, WHE is used to analyze the stochastic non-damped oscillatory equation. The corresponding deterministic system is obtained, and solution techniques are suggested and compared. The solution statistics are computed in analytical formulae and compared for different parameters. The efficiency of WHE is outlined as a reliable technique that can be used for any order of approximation in linear and nonlinear SDEs.

Keywords:Linear stochastic differential equations; Wiener-hermite expansion; Linear oscillatory; WHEP technique; Mathematical

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